Question 468221
Bobby takes x hours
so he does 1/x of the job in 1 minute

Billy mows in x-15 minutes
so he does 1/(x-15)of the job in 1 minute

together they do in 69 minutes
so they do 1/69 of the job in 1 minute

{{{1/x + 1/(x-15) = 1/69}}}

LCD = 69x(x-1)
Multiply the equation by the LCD

{{{69(x-1)+ 69x= x(x-1)}}}

69x-69+69x=x^2-x

x^2-x-138x=-69

x^2-139x+69=0

Find the roots of the equation by quadratic formula							
							
a=	1	,b=	-139	,c=	69		
							
b^2-4ac=	19321	-276				
b^2-4ac=	19045						
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-12+sqrt(24))/(12)}}}							
x1=(	139	+	138	)/	2		
x1=	138.5						
x2=(	139	-138	) /	2			
x2= 	0.5		

Bobby takes 138.5 minutes
Billy takes 125.5 minutes